Frequency of a String

Calculates the string frequency from diameter, length, density and tension of a string (or chord). A string oscillates, when being drawn (e.g. violin), plucked (e.g. guitar) or struck (e.g. piano), with a certain fundamental frequency and, in theory, infinite many harmonic overtones, which are integer multiples of the fundamental frequency. Those frequencies result from the physical properties of the string. The fundamental frequency determines the note, the ratios of the strengths of the overtones determine the timbre, which can't be calculated here. Wavelength and spread velocity refer to the fundamental frequency.

Diameter d:

Length l:

Density ρ:

kg/m³

Tension ψ:

N

Fundamental frequency f:

Hz

Wavelength λ:

m

Spread velocity c:

m/s

1. overtone f1:

Hz

2. overtone f2:

Hz

3. overtone f3:

Hz

4. overtone f4:

Hz

5. overtone f5:

Hz

Please enter the first four values, the others will be calculated.

The formula for the frequency is: f = √ ψ / ( π * ρ ) / ( d * l )

The formula for the spread velocity is: c = 2 * f * l = λ * f

The wavelength of the fundamental frequency λ is twice the string length.

The unit for the tension is newton, for the frequencies the unit is hertz.